Total Questions:50 Total Time: 60 Min
Remaining:
Question:If \({\sin ^2}\theta = \frac{1}{4},\)then the most general value of \(\theta \)is
\(2n\pi \pm {( - 1)^n}\frac{\pi }{6}\)
\(\frac{{n\pi }}{2} \pm {( - 1)^n}\frac{\pi }{6}\)
\(n\pi \pm \frac{\pi }{6}\)
\(2n\pi \pm \frac{\pi }{6}\)
Question:If \({\sec ^2}\theta = \frac{4}{3}\), then the general value of \(\theta \)is
\(2n\pi \pm \frac{\pi }{3}\)
\(n\pi \pm \frac{\pi }{3}\)
Question:General solution of the equation \(\cot \theta - \tan \theta = 2\)is
\(n\pi + \frac{\pi }{4}\)
\(\frac{{n\pi }}{2} + \frac{\pi }{8}\)
\(\frac{{n\pi }}{2} \pm \frac{\pi }{8}\)
None of these
Question:If \(\cot \theta + \tan \theta = 2{\rm{cosec}}\theta \), the general value of \(\theta \) is
Question:If \({\tan ^2}\theta - (1 + \sqrt 3 )\tan \theta + \sqrt 3 = 0\), then the general value of \(\theta \) is
\(n\pi + \frac{\pi }{4},n\pi + \frac{\pi }{3}\)
\(n\pi - \frac{\pi }{4},n\pi + \frac{\pi }{3}\)
\(n\pi + \frac{\pi }{4},n\pi - \frac{\pi }{3}\)
\(n\pi - \frac{\pi }{4},n\pi - \frac{\pi }{3}\)
Question:The most general value of \(\theta \)satisfying the equations \(\sin \theta = \sin \alpha \)and \(\cos \theta = \cos \alpha \)is
\(2n\pi + \alpha \)
\(2n\pi - \alpha \)
\(n\pi + \alpha \)
\(n\pi - \alpha \)
Question:The solution of the equation \(4{\cos ^2}x + 6\)\({\sin ^2}x = 5\)
\(x = n\pi \pm \frac{\pi }{2}\)
\(x = n\pi \pm \frac{\pi }{4}\)
\(x = n\pi \pm \frac{{3\pi }}{2}\)
Question:If \(\sin 3\alpha = 4\sin \alpha \sin (x + \alpha )\sin (x - \alpha ),\)then \(x = \)
\(n\pi \pm \frac{\pi }{4}\)
\(n\pi \pm \frac{\pi }{2}\)
Question:If \(\sin {\rm{ }}\left( {\frac{\pi }{4}\cot \theta } \right) = \cos {\rm{ }}\left( {\frac{\pi }{4}\tan \theta } \right)\,\,,\) then \(\theta = \)
\(2n\pi \pm \frac{\pi }{4}\)
\(n\pi - \frac{\pi }{4}\)
Question:If \(\sin 2\theta = \cos 3\theta \)and \(\theta \)is an acute angle, then \(\sin \theta \)is equal to [
\(\frac{{\sqrt 5 - 1}}{4}\)
\(\frac{{ - \sqrt 5 - 1}}{4}\)
0
Question:If \(4{\sin ^4}x + {\cos ^4}x = 1,\)then x =
\(n\pi \)
\(n\pi \pm {\sin ^{ - 1}}\frac{2}{5}\)
\(n\pi + \frac{\pi }{6}\)
Question:If \(\cos 3x + \sin \left( {2x - \frac{{7\pi }}{6}} \right) = - 2\), then \(x = \) (where \(k \in Z\))
\(\frac{\pi }{3}(6k + 1)\)
\(\frac{\pi }{3}(2k + 1)\)
Question:The equation \({\sin ^4}x + {\cos ^4}x + \sin 2x + \alpha = 0\)is solvable for
\( - \frac{1}{2} \le \alpha \le \frac{1}{2}\)
\( - 3 \le \alpha \le 1\)
\( - \frac{3}{2} \le \alpha \le \frac{1}{2}\)
\( - 1 \le \alpha \le 1\)
Question:If \(|k|\, = 5\)and \({0^o} \le \theta \le {360^o}\), then the number of different solutions of 3\(\cos \theta + 4\sin \theta = k\) is
Zero
Two
One
Infinite
Question:If \(0 \le x \le \pi \)and \({81^{{{\sin }^2}x}} + {81^{{{\cos }^2}x}} = 30\), then x =
\(\pi /6\)
\(\pi /2\)
\(\pi /4\)
\(3\pi /4\)
Question:If \(\sin \theta = \sqrt 3 \cos \theta , - \pi < \theta < 0\), then \(\theta = \)
\( - \frac{{5\pi }}{6}\)
\( - \frac{{4\pi }}{6}\)\(\)
\(\frac{{4\pi }}{6}\)
\(\frac{{5\pi }}{6}\)
Question:The only value of x for which \({2^{\sin x}} + {2^{\cos x}} > {2^{1 - (1/\sqrt 2 )}}\) holds, is
\(\frac{{5\pi }}{4}\)
\(\frac{{3\pi }}{4}\)
\(\frac{\pi }{2}\)
All values of x
Question:If \((1 + \tan \theta )(1 + \tan \varphi ) = 2\), then \(\theta + \varphi \)=
\({30^o}\)
\({45^o}\)
\({60^o}\)
\({75^o}\)
Question:Period of \(|2\sin 3\theta + 4\cos 3\theta |\)is
\(\frac{{2\pi }}{3}\)
\(\pi \)
\(\frac{\pi }{3}\)
Question:The period of \({\sin ^4}x + {\cos ^4}x\)is
\(2\pi \)
\(3\pi /2\)
Question:If the angles of a triangle \(ABC\)be in A.P., then
\({c^2} = {a^2} + {b^2} - ab\)
\({b^2} = {a^2} + {c^2} - ac\)
\({a^2} = {b^2} + {c^2} - ac\)
\({b^2} = {a^2} + {c^2}\)
Question:In triangle \(ABC\), \((b + c)\cos A + (c + a)\cos B\) \( + (a + b)\cos C = \)
1
\(a + b + c\)
\(2(a + b + c)\)
Question:\(\angle A + \angle C = {90^o}\)In\(\Delta ABC,\) if \(2(bc\cos A + ca\cos B + ab\cos C) = \)
\({a^2} + {b^2} + {c^2}\)
Question:In \(\Delta ABC,\) \({\rm{cosec }}A(\sin B\cos C + \cos B\sin C) = \)
\(c/a\)
\(a/c\)
\(c/ab\)
Question:In \(\Delta ABC\), \(c\cos (A - \alpha ) + a\cos (C + \alpha ) = \)
\(a\cos \alpha \)
\(b\cos \alpha \)
\(c\cos \alpha \)
\(2b\cos \alpha \)
Question:In \(\Delta ABC\), \(\frac{{\cos A}}{a} + \frac{{\cos B}}{b} + \frac{{\cos C}}{c} = \)
\(\frac{{{a^2} + {b^2} + {c^2}}}{{abc}}\)
\(\frac{{{a^2} + {b^2} + {c^2}}}{{2abc}}\)
\(\frac{{2({a^2} + {b^2} + {c^2})}}{{abc}}\)
Question:If the angles \(A,B,C\)of a triangle are in A.P. and the sides \(a,b,c\) opposite to these angles are in G. P. then \({a^2},{b^2},{c^2}\) are in
A. P.
H. P.
G. P.
Question:If the sides of a triangle are p,q and\(\sqrt {{p^2} + pq + {q^2}} \), then the biggest angle is
\(2\pi /3\)
\(5\pi /4\)
\(7\pi /4\)
\(5\pi /3\)
Question:The perimeter of a \(\Delta ABC\)is 6 times the arithmetic mean of the sines of its angles. If the side a is 1, then the angle A is
\(\frac{\pi }{6}\)
Question:Point D, E are taken on the side BC of a triangle \(ABC\)such that \(BD = DE = EC\).If \(\angle BAD = x\), \(\angle DAE = y\), \(\angle EAC = z\), then the value of \(\frac{{\sin (x + y)\sin (y + z)}}{{\sin x\sin z}} = \)
2
4
Question:If in a triangle ABC side \(a = (\sqrt 3 + 1)\)cms and \(\angle B = {30^o},\) \(\angle C = {45^o}\), then the area of the triangle is
\(\frac{{\sqrt 3 + 1}}{3}c{m^2}\)
\(\frac{{\sqrt 3 + 1}}{2}c{m^2}\)
\(\frac{{\sqrt 3 + 1}}{{2\sqrt 2 }}c{m^2}\)
\(\frac{{\sqrt 3 + 1}}{{3\sqrt 2 }}c{m^2}\)
Question:If in a right angled triangle the hypotenuse is four times as long as the perpendicular drawn to it from opposite vertex, then one of its acute angle is
\({15^o}\)
Question:In a\(\Delta ABC,\)if \(b = 20,c = 21\)and \(\sin A = 3/5\), then \(a = \)
12
13
14
15
Question:Let D be the middle point of the side BC of a triangle ABC. If the triangle ADC is equilateral, then \({a^2}:{b^2}:{c^2}\)is equal to
\(1:4:3\)
\(4:1:3\)
\(4:3:1\)
\(3:4:1\)
Question:If the sides of triangle be 6, 10 and 14 then the triangle is
Obtuse angled
Acute angled
Right angled
Equilateral
Question:In any \(\Delta ABC\)if \(a\cos B = b\cos A\), then the triangle is
Equilateral triangle
Isosceles triangle
Scalene
Question:If A is the area and 2s the sum of 3 sides of triangle, then
\(A \le \frac{{{s^2}}}{{3\sqrt 3 }}\)
\(A \le \frac{{{s^2}}}{2}\)
\(A > \frac{{{s^2}}}{{\sqrt 3 }}\)
Question:If in a triangle \(ABC\)right angled at \(B,s - a = 3\), \(s - c = 2\), then the values of a and c are respectively
2, 3
3, 4
4, 3
6, 8
Question:The area of triangle \(ABC,\) in which \(a = 1,\;b = 2\), \(\angle C = 60^\circ \)is
\(\frac{1}{2}\)
\(\sqrt 3 \)
\(\frac{{\sqrt 3 }}{2}\)
\(\frac{3}{2}\)
Question:In a triangle \(ABC\), if \(b + c = 2a\) and \(\angle A = 60^\circ ,\) then \(\Delta ABC\) is
Isosecles
Question:In any triangle ABC, \(a\cot A + b\cot B + c\cot C = \)
\(r + R\)
\(r - R\)
\(2(r + R)\)
\(2(r - R)\)
Question:If the radius of the circumcircle of an isosceles triangle \(PQR\) is equal to \(PQ( = PR),\)then the angle P is
Question:The angle of elevation of a tower at a point distant d meters from its base is\({\rm{3}}0^\circ \). If the tower is 20 meters high, then the value of d is
\(10\sqrt 3 m\)
\(\frac{{20}}{{\sqrt 3 }}m\)
\(20\sqrt 3 m\)
\(10\)m
Question:The angle of elevation of the top of the tower observed from each of the three points \(A,B,C\)on the ground, forming a triangle is the same angle \(\alpha \). If R is the circum-radius of the triangle ABC, then the height of the tower is
\(R\sin \alpha \)
\(R\cos \alpha \)
\(R\cot \alpha \)
\(R\tan \alpha \)
Question:From a point a metre above a lake the angle of elevation of a cloud is a and the angle of depression of its reflection is \(\beta \). The height of the cloud is
\(\frac{{a\sin \,(\alpha + \beta )}}{{\sin \,(\alpha - \beta )}}\)
metre\(\frac{{a\sin \,(\alpha + \beta )}}{{\sin \,(\beta - \alpha )}}\) metre
\(\frac{{a\sin \,(\beta - \alpha )}}{{\sin \,(\alpha + \beta )}}\) Metre
Question:If the angle of depression of a point A on the ground from the top of a tower be \(30^\circ \), then the angle of elevation of the top of the tower from the point A will be
\(60^\circ \)
\(45^\circ \)
\(30^\circ \)
Question:The angle of depression of a ship from the top of a tower 30 metre high is \({60^0}\), then the distance of ship from the base of tower is [MP PET 1988; Pb. CET 2003]
30 m
\(30\,\sqrt 3 \,\,m\)
\(10\sqrt 3 \,m\)
10 m
Question:The angle of elevation of a stationary cloud from a point 2500 m above a lake is \({15^0}\) and the angle of depression of its reflection in the lake is \({45^0}\). The height of cloud above the lake level is
\(2500\,\sqrt 3 \,metres\)
2500 metres
\(500\,\sqrt 3 \,metres\)
Question:A person is standing on a tower of height \(15(\sqrt 3 + 1)\,m\) and observing a car coming towards the tower. He observed that angle of depression changes from \({30^0}\) to \({45^0}\) in 3 sec. What is the speed of the car
36 km/hr
72 km/hr
18 km/hr
30 km/hr
Question:Two men are on the opposite side of a tower. They measure the angles of elevation of the top of the tower \({45^0}\) and \({30^0}\) respectively. If the height of the tower is 40 m, find the distance between the men
40 m
\(40\sqrt 3 \,m\)
68.280 m
109.28 m